Tính (22/1.3).(32/2.4).(42/3.5)...(1502/149.151)
22/1.3 x 32/2.4 x 42/ 3.5 x 52/4.6
Đang cần gấp,giúp tớ với aaa.Cảm ơnnn nhieuuu a
\(\dfrac{2^2}{1\times3}\times\dfrac{3^2}{2.4}\times\dfrac{4^2}{3.5}\times\dfrac{5^2}{4.6}=\dfrac{2^2.3^2.4^2.5^2}{1.3.2.4.3.5.4.6}=\dfrac{2^2.3^2.4^2.5^2}{1.2.3.3.4.4.5.2.3}=\dfrac{2^2.3^2.4^2.5^2}{3^3.2^2.4^2.5.1}=\dfrac{5}{3.1}=\dfrac{5}{3}\)
\(\dfrac{2^2}{1\cdot3}\cdot\dfrac{3^2}{2\cdot4}\cdot\dfrac{4^2}{3\cdot5}\cdot\dfrac{5^2}{4.6}\\ =\dfrac{2^2\cdot3^2\cdot4^2\cdot5^2}{1\cdot3\cdot2\cdot4\cdot3\cdot5\cdot4\cdot6}\\ =\dfrac{2^2\cdot3^2\cdot4^2\cdot5^2}{1\cdot2\cdot4^2\cdot4^2\cdot5\cdot6}\\ =\dfrac{2\cdot5}{6}=\dfrac{5}{3}\)
Trả lời đúng và xong trong vòng trưa nay nhé :Tính: 22 phần 1.3 . 32 phần 2.4 . 42 phần 3.5 ...... 992 phần 98.100
Tính B = \(\frac{2^2}{1.3}\) . \(\frac{3^2}{2.4}\). \(\frac{4^2}{3.5}\).............\(\frac{150^2}{149.151}\)
\(B=\frac{\left(2.3.4...150\right)\left(2.3.4...150\right)}{\left(1.2.3...149\right)\left(3.4.5...151\right)}\)
\(B=\frac{\left(1.2.3...149\right).150.2.\left(3.4.5...150\right)}{\left(1.2.3...149\right).\left(3.4.5...150\right).151}\)
\(B=\frac{300}{151}\)
Ơ mình làm chi tiết rồi mà nhỉ ??
1)Tính tổng 1.3+2.4+3.5+...+97.99+98.1001.3+2.4+3.5+...+97.99+98.100
B=1.3+2.4+3.5+...+97.99+98.100B=1.3+2.4+3.5+...+97.99+98.100
B=1(2+1)+2(3+1)+....+97(98+1)+98(99+1)B=1(2+1)+2(3+1)+....+97(98+1)+98(99+1)
B=1.2+1+2.3+2+....+97.98+97+98.99+98B=1.2+1+2.3+2+....+97.98+97+98.99+98
B=(1.2+2.3+3.4+....+97.98+98.99)+(1+2+3+...+98)B=(1.2+2.3+3.4+....+97.98+98.99)+(1+2+3+...+98)
B=98.99.1003+98.992B=98.99.1003+98.992
B=323400+4851=328251B=323400+4851=328251
Số đó=1.3 + 2.4 + 3.5 +....+ 98.100
= 1(2+1) + 2.(3+1) + 3.(4+1) +...+ 98(99+1)
= 1.2 + 1 + 2.3 + 2 + 3.4 + 3+....+ 98.99 +98
= (1.2 + 2.3 + 3.4+....98.99) + (1+2+3+....+98)
=323400 + 4851=328251
tính k = 1.3/3.5+ 2.4/5.7+3.5/7.9+...+1002.1004/2005.2007
Tính GTBT:1.3/3.5+2.4/5.7+3.5/7.9+...+48.50/97.99
Bài 1
A=1.2+2.3+3.4+....+151.152
B=1.3+3.5+5.7+...+2023.2025
C=2.4+4.6+...+2024.2026
D=1.2+3.4+...+200.202
M=12+22+...+20242
N=13+23+...+1003
Q=13+23+...+20243
R=12+22+...+2003
\(A=1\cdot2+2\cdot3+...+151\cdot152\)
\(=1\left(1+1\right)+2\left(1+2\right)+...+151\left(1+151\right)\)
\(=\left(1+2+3+...+151\right)+\left(1^2+2^2+...+151^2\right)\)
\(=\dfrac{151\left(151+1\right)}{2}+\dfrac{151\left(151+1\right)\left(2\cdot151+1\right)}{6}\)
\(=151\cdot76+\dfrac{151\cdot152\cdot303}{6}\)
\(=151\cdot76+151\cdot7676=1170552\)
\(C=2\cdot4+4\cdot6+...+2024\cdot2026\)
\(=2\cdot2\left(1\cdot2+2\cdot3+...+1012\cdot1013\right)\)
\(=4\left[1\left(1+1\right)+2\left(1+2\right)+...+1012\left(1+1012\right)\right]\)
\(=4\left[\left(1+2+...+1012\right)+\left(1^2+2^2+...+1012^2\right)\right]\)
\(=4\left[1012\cdot\dfrac{1013}{2}+\dfrac{1012\left(1012+1\right)\left(2\cdot1012+1\right)}{6}\right]\)
\(=4\left[506\cdot1013+345990150\right]\)
\(=1386010912\)
\(M=1^2+2^2+...+2024^2\)
\(=\dfrac{2024\left(2024+1\right)\cdot\left(2\cdot2024+1\right)}{6}\)
\(=2024\cdot2025\cdot\dfrac{4049}{6}\)
=2765871900
\(N=1^3+2^3+...+100^3\)
\(=\left(1+2+3+...+100\right)^2\)
\(=\left[\dfrac{100\left(100+1\right)}{2}\right]^2\)
\(=\left[50\cdot101\right]^2=5050^2\)
\(Q=1^3+2^3+...+2024^3\)
\(=\left(1+2+3+...+2024\right)^2\)
\(=\left[\dfrac{2024\left(2024+1\right)}{2}\right]^2\)
\(=\left[1012\left(2024+1\right)\right]^2\)
\(=2049300^2\)
Tính : A = 1.3 + 2.4 + 3.5 + ..... + 98.100
= 1.( 2 + 1 ) + 2 ( 3 + 1 ) + 3( 4 + 1 ) + ..... + 98( 99 + 1 )
= 1 . 2 + 1 + 2 . 3 + 2 + 3 . 4 + 3 + ...... 98 . 99 + 98
= ( 1 . 2 + 2 . 3 + 3 . 4 + ..... + 98 . 99 ) + ( 1 + 2 + 3 + ..... + 98 )
= 323400 + 4851
= 328351
A = 1.( 2 + 1 ) + 2.( 3 + 1 ) + 3.( 4 + 1 ) + .... + 98.( 99 + 1 )
A = 1.2 + 1 + 2.3 + 2 + 3.4 + 3 + .... + 98.99 + 98
A = ( 1.2 + 2.3 + 3.4 + .... + 98.99 ) + ( 1 + 2 + 3 + ... + 98 )
Đặt B = 1.2 + 2.3 + 3.4 + .... + 98.99
C = 1 + 2 + 3 + .... + 98
=> 3B = 1.2.3 + 2.3.3 + 3.4.3 + .... + 98.99.3
= 1.2.3 + 2.3.( 4 - 1 ) + 3.4.( 5 - 2 ) + ..... + 98.99.( 100 - 97 )
= 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 -2.3.4 + .... + 98.99.100 - 97.98.99
= 98.99.100
=> B = ( 98.99.100 ) : 3 = 323400
=> C = 1 + 2 + 3 + .... + 98
C = 98 + 97 + .... + 2 + 1
=> 2C = 99 + 99 + .... + 99 + 99
=> 2C = 99.98 = 9702
=> C = 4851
\(\Rightarrow A=323400+4851=328251\)
Tính : A = 1.3 + 2.4 + 3.5 + ..... + 98.100